A solver for aerosol condensation equation by semi-lagrangian scheme with correction exactly conserving total particle number

Semi-Lagrangian scheme (cubic polynomial semi-Lagrangian (CSL) or cubic interpolated propagation (CIP) scheme) is applied to condensation equation of cumulative number distribution, and simple correction using mathematical constrains of cumulative number distribution is applied after the semi-Lagrangian procedure at each time step. This solver exactly conserves total particle numberNand prevents overshoots of aerosol size distribution with steep gradients. The total surface areaSand the total volumeVare also easily conserved within small error. In the cases where the size distributions are not extremely sharp, CSL and CIP both can be utilized in the solver for the aerosol condensation. On the other hand, in the cases where the distributions are quite sharp, the solver using CIP gives the almost same result as the exact solution.